Alpha-Beta-Zero to abc

Table of Contents

The “Alpha-Beta-Zero to abc” block computes a three-phase (abc) signal from a space vector in a stationary reference frame (αβ0).

The transformation is performed using the following equation:

$$ \begin{bmatrix} V_a\\V_b\\V_c\end{bmatrix}
= \begin{bmatrix} 1 & 0 & 1\\-1/2 & \sqrt{3}/2 & 1\\ -1/2 & -\sqrt{3}/2 & 1\end{bmatrix}\cdot
\begin{bmatrix} V_\alpha\\V_\beta\\V_0\end{bmatrix}$$

Simulink block

Signal specification

The input is a vector of dimension 3, containing the αβ0 components of the three-phase signal in the stationary reference frame.
The output is a vector of dimension 3, containing the abc components of the three-phase signal.

Parameters

None.

PLECS block

None. The PLECS block Transformation SRF->3ph can be used instead.

C++ functions

The user template located in the installation folder of CPP SDK contains an API folder with implementations of the coordinate transformation functions. The αβ0 to abc function is the following:

void ABG2abc(TimeDomain *physical, const SpaceVector *fixed);
Code language: C++ (cpp)

Parameters

physical: pointer on the time domain abc data that will be updated. The TimeDomain structure is defined below.
fixed: pointer on the αβ0 space vector that will be transformed. The SpaceVector structure is defined below.

typedef struct{
	float real;       // alpha-axis component
	float imaginary;  // beta-axis component
	float offset;     // homopolar component
} SpaceVector;

typedef struct{
	float A;
	float B;
	float C;
} TimeDomain;Code language: C++ (cpp)